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Supplemental Information

Linker Dependent Bond Rupture Force

Measurements in Single-Molecule Junctions

M. Frei1, S Aradhya1, M. S. Hybertsen2, L. Venkataraman1

1Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027.

2Center for Functional Nanomaterials, Brookhaven National Labs, Upton, NY 11973

Email: mhyberts@bnl.gov; lv2117@columbia.edu

Contents:

1. Experimental Details 2. Data Analysis 3. Additional Data 4. Procedures for Theoretical Calculations and Results 5. References

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1. Experimental Details

Experimental Setup and Procedures: The conductive AFM consists of a modified AFM head

(Multimode Veeco), external adder and filter circuits (SRS), as well as a homebuilt cantilever

holder. A bias was applied between a gold coated, conductive cantilever (TAP300

BudgetSensors) and an Au substrate placed on top of a single-axis piezoelectric positioner with

built-in position sensor (Mad City Labs). The resulting current was converted to a voltage with a

current amplifier (Keithley 428). Data collection and control of the piezoelectric positioner were

done by means of a data acquisition board (National Instruments, PXI-4461) driven by a

customized program using Igor software (Wavemetrics Inc.). For the simultaneous conductance

and force trace measurements, the substrate approached the cantilever tip until a set conductance

larger than 5G0 was measured to ensure that the Au/molecule/Au junction from the previous

measurement was completely destroyed. For standard conductance and force measurements, the

sample was withdrawn at a rate of 18 nm/s and the current and force versus position data was

recorded at a sampling frequency of 100 kHz. All position determinations were based on

measurements with a built-in position sensor within our custom piezoelectric positioner. This

position sensor was calibrated both by the manufacturer and by us using laser interference

measurements. We found the absolute values of the measured displacements to be accurate to

within 5%.

SI Figure S1: Schematic of the AFM measurement set-up.

Cantilever Calibration details: Force resolution along the pulling direction is achieved by measuring the

deflection of a focused laser that is reflected off the back of a cantilever using a quadrant detector. The

voltage signal corresponding to the deflection of the laser is converted to force in two steps. First the

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quadrant detector signal is converted to a deflection in nm by forcing a solid contact between the sample

substrate and the cantilever and subsequently moving the substrate by a known distance using the piezo.

Second, the spring constant of the cantilever is determined using the power spectrum method1. The

voltage signal in nm is converted to a force by multiplying by the cantilever spring constant. The

determined Au-Au breaking force which is consistent with accepted values from literature2, validates our

calibration method. �

2. Data Analysis Conductance Step Detection: The molecular junction conductance step detection was carried out as

follows. First, 1D conductance histograms were computed from all measured traces for each molecule to

determine the conductance peak location and its width. This determines a minimum and maximal

conductance value for each of the molecules studied. For each measured trace, the number of data points

within this conductance range is determined. If this number of points is larger than the number required

for a 0.02 nm plateau, the plateau length and slope, normalized to the average conductance are obtained.

Traces with a conductance plateau longer than 0.02 nm and with a normalized slope larger than -5, are

selected for further analysis. For each selected trace, the end of the conductance plateau is determined,

and the conductance trace is analyzed to ensure that there was a sharp conductance drop following this

plateau. This is done by requiring that the conductance after the plateau was less than 0.2 times that of the

plateau (irrespective of the molecule type). 2D conductance and force histograms were then generated

from all selected traces.

2D Histograms: Each measured conductance and force trace consisted of data acquired every 10 µs,

measured at a constant 18 nm/s velocity. As conductance plateaus occur in random locations along the

entire displacement axis (x-axis) within the measured range for each trace, we first set the origin of our

displacement axis at the point where either the 1G0 conductance step or the molecular conductance step

breaks. This well-defined position on the x-axis is determined individually for each trace, using an

automated algorithm as described above. Each data point on the digitized conductance (force) trace now

has a conductance (force) coordinate (along the y-axis) and a position coordinate (along the x-axis). Two

dimensional conductance histograms are then generated without further analysis. For the two-dimensional

force histogram, we also set the force at the zero-displacement position to zero force by subtracting an

offset from the entire force trace. This realigns all force traces to a common point such that each force and

displacement value is now determined relative to that at the end of the conductance step in each trace.

After this re-alignment, thousands of force traces are added to generate a two-dimensional force

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histogram. A statistically averaged force profile is obtained from this histogram from the peak of a

Gaussian that is fit to vertical sections at every displacement bin.

Force Based Event Recognition Algorithm: In force based event recognition all events are identified using

force data. The goal is to determine the location of every sharp force event occurring in each trace. This is

achieved using a three step algorithm: (1) we subtract, from the raw force trace, a smoothed and laterally

offset force trace. This effectively highlights low frequency changes of the force signal. (2) We multiply

these by the square of the derivative of the original force trace. (3) The resulting trace (‘Analyzed Force’

in SI Figure S2) has sharp spikes at locations where the original force trace has sharp drops. These sharp

spikes that are larger than a cut-off are selected. The cutoff is chosen to be 20 times the standard deviation

of the Analyzed Force trace which ensures that selected spikes are significantly larger than small

deviations in the Analyzed Force due to measurement noise. SI Figure S2 shows a sample conductance

(red) and force (blue) trace that has been analyzed in this manner. It also shows, in black, the Analyzed

Force trace where all drops are identified for gold point contact. For each measurement, the location of

each spike along with the force and conductance right before and right after is recorded. For illustration,

in the example of breaking a single-atom gold point contact, the conductance before the identified force

event would be close to the quantum of conductance (G0) and that right after would be below G0.

SI Figure S2: Force based event recognition illustrated for a gold point contact. The analyzed force

trace (black) effectively highlights the force events, and the multi-fit procedure accurately determines the

force before (green square) and after (green diamond).

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Force traces are further analyzed to make sure that each event identified exhibits a well-defined saw-tooth

signature. For a given force event, we fit three-line segment around the rupture location as shown in SI

Figure S3. We select the fit with the lowest error from 400 different fit combinations where the end of

line segment one (X1) and beginning of line segment 3 (X2) are varied in 20 incremental steps of 0.0006

nm along the displacement axis. This iterative fitting mechanism is more accurate in determining the

location of rupture events which are often not correctly identified within a distance of 0.004 nm. In order

to further eliminate fitting inaccuracies we also exclude traces for which the end of the first line segment

(X1) occurs after the start of the third line segment (X2) and traces for which the middle segment has a

positive slope (SI Figure S3). Finally the numerical value of each rupture is taken as the difference

between the value of fit at X1 and X2.

SI Figure S3: A schematic of the force based event recognition fitting procedure. 400 three segment lines

(1,2,3) are fit to the force event by varying X1 and X2 incrementally and the one with the smallest error is

chosen.

Histograms of rupture forces are generated. A Gaussian fit is used to determine a most likely breaking

force for the particular bond breaking under consideration. By comparison with our conductance based

event identification method, we find good agreement for the average rupture force. The main limitation to

this method is that small force events are hard to reliably distinguish from the background noise. From

our conductance based analysis, we have found that small force events are statistically meaningful when

evaluating the average breaking force. Therefore, the purely force-based method may overestimate the

average breaking force.

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Additional Data:

SI Figure S4: (A) 2D conductance histogram (15542 traces) for clean gold traces showing quantized

steps above 1G0 and a clean break to experimental noise. (B) 2D force histogram for the simultaneously

measured force traces showing the force profile in red indicating a most probable breaking force for the

gold-gold bond of 1.4 nN.

SI Figure S5: (A) 2D conductance histogram (3544 traces) for C4NH2 showing quantized steps above

1G0 and a typical molecular signature at around 10-3 G0. Inset: sample conductance trace (B) 2D force

histogram for the simultaneously measured force traces. The average force profile (black) indicates a

breaking force of 0.6 nN. Inset: sample force trace.

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SI Figure S6: (A) 2D conductance histogram (1694 traces) for C5DPP showing quantized steps above

1G0 and a typical molecular signature for C5DPP at around 6.6×10-4 G0. Inset: sample conductance

trace. (B) 2D force histogram for the simultaneously measured force traces. The average force profile

(black) indicates a breaking force of 0.8 nN. Inset: sample force trace

SI Figure S7. One dimensional conductance histograms for C4SMe (green, 10000 traces) and C4SH

(black, 14000 traces). (A) Histograms created using linear bins of size 0.00001 G0. (B) Log-binned

histograms created using 100 bins per decade.

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SI Figure S8: Histograms of maximum force events per trace with conductance values consistent with

molecular features for C4SMe (green, 10092 events, peak at 0.9 nN) and C4SH (black, 22888 events,

peak at 1.2 nN).

4. Procedures for Theoretical Calculations and Results

We use density functional theory (DFT) based calculations to simulate the junction elongation and rupture

process for several links studied here, following the procedure outlined3. Briefly, the Au tip and surface

were modeled with Au pyramids (20 atoms each) with (111) surfaces. The tip atom on the top pyramid

was moved to an adatom site on one facet resulting in a blunt, three atom tip. The junction was elongated

from near a local energy minimum through the inflection point and finally probed the dissociated

structure after one bond ruptures. The back layer of Au atoms in each pyramid was held fixed with a bulk

lattice parameter 4.08 Å. All other degrees of freedom were relaxed until all forces were less than 0.005-

0.01 eV/Å for each junction structure. The junction was elongated in steps of 0.1 Å by increasing the

separation between the pyramids along the z direction and then fully optimizing the geometry. Density

functional theory total energy calculations and geometry optimization were performed with the VASP

package4, using the projector augmented wave approach which naturally included scalar relativistic

effects for gold5,6 and the generalized gradient approximation (GGA) of Perdew, Burke and Ernzerhof

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(PBE)7 for the exchange-correlation density functional. The model junction was placed in a hexagonal

supercell (a=2.0nm, c=3.5nm) and the basis set for solution of the Kohn-Sham equations was determined

by a 400 eV cutoff. The total energy and applied force computed from adiabatic junction elongation

trajectories for each C4SMe is shown in SI Figure S9. A simplified structure was used to compare

maximum sustained force between SMe and SH by focusing on half of the junction (Figure S10). In

these simulations, an ethane with a single link group bonded to a single tip is studied by systematically

moving the molecule upwards relative to the tip, holding the vertical position of the S atom fixed.

SI Figure S9: (A) Calculated total energy curve from an adiabatic trajectory for C4SMe shown as a

function of displacement. Bar shown at right indicates the asymptotic value. (B) Calculated applied force

curve for the same molecule shown against displacement. (C) C4SMe junction structure for displacement

near the local energy minimum.

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SI Figure S10: (A) Calculated total energy and (B) force curves from a one-sided junction structure (C

and D) comparing the SMe and SH donor-acceptor bond rupture forces. Initial geometry as illustrated

in (C) and (D), with the bond aligned to vertical. Displacement is controlled by fixing the position of the

back plane of Au atoms in the cluster modeling the electrode and the S atom bonded to the Au tip atom.

Finally, similar studies were performed for ethanethiolate model structures bonded to 21 atom gold tips

(Figure S11). An initial structure was designed to probe the maximum sustainable force under ideal

conditions of near vertical elongation along the S-Au bond, with the Au link atom bonded to three Au

atoms in the next layer. The upper C atom and one of the C-H bonds is held fixed to maintain backbone

orientation and overall elongation. This structure sustains 1.9 nN before substantial plastic rearrangement

of the tip structure. The second structure explores the rupture process when the Au link atom is

minimally coordinated, being bonded to a single Au atom on the tip. In this example, there is minimal

shear force on the tip and the structure ruptures at the Au-Au bond with a maximum sustained force of

less than 1.4 nN. This is somewhat smaller than the typical Au-Au rupture force in gold point contact

DFT simulations (1.6 nN) 8,9. Trajectories with larger shear force on the tip structure resulted in plastic

deformation of these small model tip structures.

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SI Figure S11: (A) Calculated total energy and (B) force curves from a one-sided junction structure (C

and D) comparing two thiolate elongation scenarios. Initial geometry as illustrated in (C) and (D).

Displacement is controlled by fixing the position of the back plane of Au atoms in the cluster modeling the

electrode and the upper C atom as well as the C-H bond aligned to the ethane backbone. The reference

tip structure for (C) has an Au atom on the side of the tip while for (D) the tip structure after rupture is

the ideal pyramid.

5. References

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